Space-Adiabatic Perturbation Theory in Quantum Dynamics

Gianluca Panati; Herbert Spohn; Stefan Teufel

doi:10.1103/PhysRevLett.88.250405

Space-Adiabatic Perturbation Theory in Quantum Dynamics

Gianluca Panati, Herbert Spohn, and Stefan Teufel

Phys. Rev. Lett. 88, 250405 – Published 11 June 2002

Abstract

A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schrödinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders, and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications, we discuss the Born-Oppenheimer theory to second order and derive for the first time the nonperturbative definition of the $g$ factor of the electron within nonrelativistic quantum electrodynamics.

Received 28 January 2002

DOI:https://doi.org/10.1103/PhysRevLett.88.250405

Authors & Affiliations

Gianluca Panati^*, Herbert Spohn^†, and Stefan Teufel^‡

Zentrum Mathematik and Physik Department, TU München, D-80290 München, Germany

^*Also at Mathematical Physics Sector, SISSA, Trieste, Italy. Electronic address: panati@sissa.it
^†Electronic address: spohn@ma.tum.de
^‡Electronic address: teufel@ma.tum.de